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Plotting Surfaces In Parametric Form

Surfaces which are in `z' or implicit form can often be rewritten in parametric form and pictures obtained using the parametric form are usually better. In addition, many surfaces can only be written in parametric form. Surfaces in parametric form are given as

e.g. the ellipsoid can be rewritten in parametric form using `pseudo' spherical coordinates u,v

which is plotted using

plot3d( [ 2*cos(u)*sin(v), 3*cos(u)*sin(v), 2*sqrt(2)*cos(v)], Line Feed
        u=0..2*Pi, v=0..Pi );
From Axes choose Boxed and then rotate the picture to get a better view. Compare this with the picture obtained using implicitplot3d. Also, notice the axes are divided but not labeled - can you point out the x, the y, and the z axes?

The parametric form of the cone is obtained by rewriting it in cylindrical coordinates as i.e. where r is non-negative. So one of its parametric forms is

Now plot this as shown above - remember the Maple command for absolute value is abs. The above surface may also be plotted using the commands cylinderplot or sphereplot in the plots package. Use Maple's help facility for more details.



Peter Monk
Tue Aug 29 14:41:29 EDT 1995